The invention relates to a method for generating a digital lookup table for printing inks in image reproduction equipment using color scan values obtained by photoelectric scanning of an original.
The basis for generation of a transformation table for the primary colors "RGB" into the complementary colors "CMYK" is spectrophotometric measurement of a color scale generated with that process (e.g. Offset, Euroskala, coated paper) for which this table is later to apply. With unlimited expenditure, it would be possible to thereby obtain by measurement the right field for every required color stimulus from a scale with 1% gradation of the printing inks, i.e. 100*100*100 color fields. A method of this type would provide, if the color range of the scale is not always exceeded, the formula for the complementary colors "CMYK" accurate to 1%. Highly saturated hues have no corresponding field. In addition, one million measurements are impracticable for generating a table.
A color correction device for image reproduction equipment is known with which digitalized color density values of individual color separations obtained by photoelectric scanning are converted into complementary color density values. With the complementary color density values it is possible to obtain color separation negatives. The complementary color density values are color-corrected using correction data filed in a memory and addressable and outputtable by the color density values. A gray component is determined from the color density values. This is achieved by comparing the color density values. The gray component is processed by comparison with a predetermined white light value to obtain an equivalent gray value with which a memory is addressed that contains a specific gray value for each complementary color density value. By subtracting the gray components from the color density values, complementary color density values are generated. The various complementary color density values are each combined with an associated specific gray value. Corrections to the chromatic component and to the gray component independently of one another permit a saving of memory capacity for the conversion table (German patent DE-PS 30 15 396).
One of the objects underlying the invention is to develop a method for generation of a digital lookup table (memory table) of complementary printing inks for image reproduction equipment using standardized color scan values obtained by photoelectric scanning of an original, e.g. EBU red, green, blue. With the method of the invention a lookup table can be produced from a few measurement fields that is sufficiently accurate for determining the proportions of printing inks. In addition, non-reproducible color stimuli must be adapted to useful substitute values.
The object is substantially achieved in accordance with the invention in that the full colors of the three printing inks and white are measured by scanning of corresponding originals, in that model colors are determined which are in as linear as possible a relationship to the printing inks by means of a position of the chromaticity range of the print scale such that the primary stimuli of the model colors in the chromaticity diagram are each on one beam of the trajectories of the scale colors through the white point while the triangle set up between the primary stimuli encloses the chromaticity range of the print scale. The scale division of the primary stimuli is adjusted with the cube root to a linear gradation of the printing inks. The space diagonals of the printing inks as a function of the model colors are used to determine the number of fields to be scanned, scan values of which are further processed by cubic spline interpolation with a higher number of support points in order to generate the lookup table. The values of the model colors are each stored as a function of the printing ink values.
A lookup table of the printing inks as a function of the model colors is preferably generated from the stored lookup table. The latter table is used in the reproduction equipment to determine the proportions of printing inks for the original artwork measured values.
A substantial element of the invention is based on the setup of a computation model whose coordinate axes tally as closely as possible with the axes of the print scale (cyan, magenta and yellow). A component of the model color space depends in largely linear form on one and one only printing ink. The CIE-XYZ color space of the International Lighting Commission does not--unlike the model color space described above--fulfill these requirements, since the directions of its coordinate axes do not even approximately tally with those of the primary stimuli of the print scale. Particularly unfavorable is the fact that identically sized color intervals at different points on the print scale are reproduced on variously sized differences in the CIE-XYZ color space. The aforementioned substitute colors C.sub.t, M.sub.t and Y.sub.t describe the printing inks approximately and can be advantageously converted as a group into values of the CIE-XYZ color space. The relationship C.sub.t =1-R makes the substitute color stimulus C.sub.t proportional to the color stimulus C.sub.s. Weighting with the cube root linearizes the dependence of the model color on the printing ink. The conversion between the coordinates of the RGB color space and of the CIE-XYZ color space and vice versa is achieved in each case with a transformation matrix that is known per se (Richter: Einfuhrung in die Farbmetrik, Kap. 6).
The expense of creating a print scale depends on the number of fields to be measured. An acceptable expenditure is achieved when the number of fields to be measured is not more than a few hundred. If scan values are generated for each coordinate axis of the print scale, n.sup.3 fields must be measured. The number of scan values must ensure a sufficiently accurate coverage of the print scale.
In the space diagonals of the coordinate system of full colors C.sub.s, M.sub.s and Y.sub.s, the proportionate basic colors of the print scale are present in equal amounts. With these space diagonals as the "gray axis" conclusions can be drawn as to the remaining non-linearities of the print scale with regard to the model color space. On the basis of the dependence of the hue values on the print scale values in the "gray axis" the minimum necessary (not equidistant) scanning steps are determined. The scanning steps are selected such that points are obtained along the "gray axis" that are spread as evenly as possible and at the same time at locations with as few deviations as possible between the substitute colors.
Preferably, not more than seven scanning steps are stipulated. The n.sup.3 scan values are then extrapolated by a cubic spline interpolation to a certain number of support points greater than the number of scanning steps. It has been shown that a support point quantity of 32.sup.3 values is favorable. The cubic spline interpolation results in color cubes containing printing ink values. The subdivision of the scale space is equidistant here, i.e. a color cube with a scanning density of approx. 3% is obtained in each printing ink.
The table prepared in the manner described above gives the dependence of the color stimulus on the printing ink proportions. The table permits determination of the proportions of printing inks necessary to reproduce a color stimulus.
In a preferred embodiment, the associated combinations of printing inks for all interesting combinations of color stimuli are determined iteratively in order to generate a table giving the proportions of the printing inks C.sub.s, M.sub.s and Y.sub.s needed to reproduce a color stimulus, by proceeding from any point in the print scale table to first compute both the difference between the color stimulus required and a random scale entry point, and the complete differential in this point in order to ascertain a vector that gives, in scale increments, the amount and direction of the transition to another entry point better suited to the required color stimulus. For this scale entry point appropriate computation steps are taken to establish a further vector that gives the transition to a scale entry point better suited to the required color stimulus. The computation steps for ascertaining additional scale entry points are repeated until the scale entry point obtained remains the same. Color value differences still remaining are minimized by trilinear interpolation. Using this method, which can be designated as inversion, a lookup table table for RGB or for any colors based on CIE-XYZ coordinates to CMY is obtained.
It may be that a color stimulus is required that is outside the chromaticity range of the measured print scale. The iteration process provides for such color stimuli, for one or more colors, a dot percentage of &gt;100% and/or &lt;0%. These are highly saturated colors that cannot be reproduced. However, in order nevertheless to reproduce color stimuli for inks outside the chromaticity range of the measured print scale, it is expedient to employ another color model based on hue, saturation and lightness (HSL color model). If the iteration process leaves the color space of the lookup table, then it is advantageous to correct the required color stimulus with reference to the nearest color stimulus feasible with the lookup table. While a change in the hue should not occur, correction may result in a substitute color having a lower saturation in the case of very bright or very dark hues, and possibly a slightly different lightness.
In order to determine the printing inks for a color stimulus outside the chromaticity range of the measured lookup table, a color space corresponding to the lab model stipulated by the International Lighting Commission (CIE) is computed as follows for hue, saturation and lightness: ##EQU1## with X.sub.0, Y.sub.0 and Z.sub.0 as the color stimulus of the white point (cf. DIN 6174), in which "L" means the lightness, "H" the hue, "S" the saturation and "X Y Z" the virtual primary stimuli as normal stimuli, where the corresponding values for lightness, hue and saturation are filed in a table with one address space for each, with stipulation of the maximum lightness value for maximum fluctuations of the primary stimuli and with standardization of the saturation to the maximum value occurring in the blue hues, and where for all combinations of hue, saturation and lightness occurring, the values of the printing inks are determined by iteration and then stored. In this way, the point at which the required color value leaves the range of the lookup table can only be determined as a function of the saturation. All saturations above this value can then be allocated the printing ink triplet of the last color value achieved with constant lightness and constant hue.
For obtaining print results in dark hues, a black separation is preferably generated that has been obtained using a densitometer from a test form having that number of chromatic gray bars of which each contains a constant black component, where the color density values are converted to lightnesses and where a spline interpolation increases the data density until the dependence of lightness decrease on the addition of black is given in predetermined steps for each three-color lightness level. If a hue can no longer be achieved in three colors with saturation at the predetermined lightness, transition to the next highest lightness level that the hue can reproduce follows, and the lightness is then reduced by addition of black to the required value.
To save on memory capacity, the lookup table of the printing inks is not addressed directly through the measured color stimuli. The primary colors are divided in each case into a number of classes of representative values stored in a separate table. Starting from this separate table, the three-dimensional table with the printing inks is controlled, which for that reason needs only the number of memory places corresponding to the cubic number of the number of classes. The number of classes is preferably adjusted to the human visual sense curve by dividing the primary stimuli into ranges of equal size under the cube root.
It must be noted in particular that a change in the lightness .DELTA.L takes place as a function of black (.DELTA.L=f(K)).
A device for implementation of the method described above contains in accordance with the invention a light source and a measuring head to which is connected a spectrophotometer connected on its output side to a sequential control and to a color transformer, to which is connected a cubic spline interpolator controlled by the sequential control, and to which is connected a digital memory controlled by the sequential control. The sequential control is preferably a central computer.